Transverse and Longitudinal Waves (HSC SSCE Physics): Revision Notes

Transverse and Longitudinal Waves

Introduction

Waves can be classified into different types based on how the particles in the medium move as the wave passes through. The two most commonly observed types of waves are transverse waves and longitudinal waves. Understanding the difference between these wave types is essential for studying wave behaviour and properties.

Transverse waves

What are transverse waves?

In a transverse wave, particles within the material oscillate perpendicular to the direction in which the wave is travelling. This means if the wave is moving horizontally, the particles move up and down (or side to side) as the wave passes through.

As a transverse wave travels through a medium, it creates a pattern of crests (high points) and troughs (low points) that move through the material. The particles themselves do not travel with the wave; they simply oscillate about their rest position.

Particle motion in transverse waves

The motion of particles in a transverse wave follows a specific pattern:

• At a crest or trough: Particles are momentarily stationary (not moving) and are about to reverse direction back towards their rest position
• Between crests and troughs: Particles are moving perpendicular to the direction the wave is travelling
• Complete cycle: Each particle completes one full up-and-down oscillation as one wavelength passes

The wavelength ($\lambda$) is the distance between two consecutive crests or two consecutive troughs. The displacement refers to how far a particle is from its rest position at any given moment.

Reflection of transverse waves

When a transverse wave reaches the end of the medium it is travelling through (such as a spring or string), it reflects back. The behaviour of this reflection depends on how the end is secured:

Fixed end reflection:

• If the end of the spring or string is fixed (cannot move), a crest reflects as a trough
• The wave is inverted or turned upside down upon reflection
• This is called phase inversion

Free end reflection:

• If the end is free to move up and down (such as attached to a loose ring), a crest reflects as a crest
• The wave reflects upright with no inversion
• The wave maintains its original orientation

Longitudinal waves

What are longitudinal waves?

In a longitudinal wave, particles oscillate in a direction parallel to the energy flow. This means particles move back and forth along the same line that the wave is travelling.

Unlike transverse waves which create crests and troughs, longitudinal waves create regions of compression and rarefaction as they travel through a medium.

Compressions and rarefactions

Compression:

• A region where particles are crowded together
• Occurs when particles around a point all move towards that point
• This creates a region of maximum pressure

Rarefaction:

• A region where particles are spread apart
• Occurs when particles around a point all move away from that point
• This creates a region of minimum pressure

As a longitudinal wave passes through a medium, any given point experiences a series of alternating compressions and rarefactions. The wavelength ($\lambda$) is the distance between two consecutive compressions or two consecutive rarefactions.

Comparing transverse and longitudinal waves

Key differences

The fundamental difference between these two wave types is the direction of particle motion relative to wave propagation:

Feature	Transverse Waves	Longitudinal Waves
Particle motion	Perpendicular to wave direction	Parallel to wave direction
Pattern created	Crests and troughs	Compressions and rarefactions
Pressure variation	Not applicable	Maximum at compressions, minimum at rarefactions
Can travel through gases/liquids	No (not effectively)	Yes
Examples	Waves on strings, water surface waves, electromagnetic waves	Sound waves, seismic P-waves

Why transverse waves cannot travel through fluids

Longitudinal waves can pass through gases and liquids, but transverse waves cannot propagate effectively through these substances. This is because:

• Transverse waves require the medium to transmit sideways forces (forces perpendicular to the direction of wave travel)
• Gases and liquids cannot effectively transmit these sideways forces because their particles are not rigidly connected
• The particles in fluids can slide past each other easily, preventing the transmission of transverse oscillations

Investigation: Comparing wave types

Aim

To observe and compare the motion of particles in transverse and longitudinal waves using a spring.

Safety considerations

Risk	Safety Measures
The spring may flick back into your eye if released	Wear safety glasses when working with springs. Do not over-stretch the spring

Key observations

For transverse pulses:

• Create by giving the spring a quick sideways shake
• Observe that coils move perpendicular to the pulse direction
• Note the reflection behaviour at the fixed end

For longitudinal pulses:

• Create by making a rapid back-and-forth movement along the spring direction
• Observe that coils move parallel to the pulse direction
• Identify regions of compression and rarefaction

Calculating wave speed

The speed of a wave can be calculated using:

$v = \frac{d}{t}$

where:

• $v$ = wave speed (m/s)
• $d$ = distance travelled (m)
• $t$ = time taken (s)

Remember!